A construction of noncontractible simply connected cell-like two-dimensional Peano continua
Tom 195 / 2007
Fundamenta Mathematicae 195 (2007), 193-203
MSC: Primary 54F15, 54G15, 57N60; Secondary 54C55, 55M15, 55Q52.
DOI: 10.4064/fm195-3-1
Streszczenie
Using the topologist sine curve we present a new functorial construction of cone-like spaces, starting in the category of all path-connected topological spaces with a base point and continuous maps, and ending in the subcategory of all simply connected spaces. If one starts from a noncontractible $n$-dimensional Peano continuum for any $n>0$, then our construction yields a simply connected noncontractible $(n + 1)$-dimensional cell-like Peano continuum. In particular, starting from the circle $\mathbb{S}^1$, one gets a noncontractible simply connected cell-like 2-dimensional Peano continuum.
